"The Federal Reserve needs those positions filled now with suitable individuals," wrote Chamber Deputy Chief Economist J.D. Foster in the post. "Senator Paul should make his point, and then allow the Senate to work its will."

The group, which represents the largest U.S. businesses, is increasingly taking on tea party candidates within the Republican Party.

At the Republican primaries being held Tuesday, the Chamber has spent $4 million to defeat tea party challengers in Idaho, Georgia, Kentucky and Oregon, according to a source familiar with the spending. (Spending records won't be released until after the election).

And two weeks ago, the Chamber's President Tom Donohue suggested, jokingly, that the GOP shouldn't run a presidential candidate unless it can pass legislation to reform immigration this year. House Republicans have yet to consider a Senate immigration bill that passed last June.

It's a far cry from 2010, when the Chamber spent $33 million to usher many tea party favorites into Congress, including Sen. Paul.

That year, the Chamber was the largest political spender to weigh in on elections, outside of the national political parties, according to the Center for Responsive Politics, a Washington research group.

Fixing education would create jobs

One of the key reasons behind the big business group's change of heart was last year's 16-day government shutdown that not only brought Washington to a standstill in 2013 but also hurt businesses and the U.S. economy.

The Chamber opposed the shutdown, but was championed by many in the tea party.

After that, Donohue pledged to "expand a pro-business majority in the House" in January.

That bill would force more congressional oversight of the independent Fed. Similar legislation was proposed by his father Ron Paul, when he was in the House during the financial crisis, and is popular in the tea party movement.